The Impact of Low-Ability Peers on Cognitive and Non-Cognitive Outcomes: Random Assignment Evidence on the Effects and Operating Channels This paper presents new experimental estimates of the impact of low-ability peers on own outcomes using nationally representative data from China. We exploit the random assignment of students to junior high school classrooms and find that the proportion of low-ability peers, defined as having been retained during primary school (“repeaters”), has negative effects on non-repeaters’ cognitive and non-cognitive outcomes. An exploration of the mechanisms shows that a larger proportion of repeater peers is associated with reduced after-school study time. The negative effects are driven by male repeaters and are more pronounced among students with less strict parental monitoring at home. Suggested citation: Xu, Di, Qing Zhang, and Xuehan Zhou. (2019). The Impact of Low-Ability Peers on Cognitive and Non-Cognitive Outcomes: Random Assignment Evidence on the Effects and Operating Channels. (EdWorkingPaper: 19-143). Retrieved from Annenberg Institute at Brown University: http://www.edworkingpapers.com/ai19-143 Di Xu University of California Irvine Qing Zhang University of California Irvine Xuehan Zhou University of California Irvine VERSION: October 2019 EdWorkingPaper No. 19-143
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The Impact of Low-Ability Peers on Cognitive and Non-Cognitive Outcomes: Random Assignment Evidence on the Effects and Operating Channels
This paper presents new experimental estimates of the impact of low-ability peers on own outcomes using nationally representative data from China. We exploit the random assignment of students to junior high school classrooms and find that the proportion of low-ability peers, defined as having been retained during primary school (“repeaters”), has negative effects on non-repeaters’ cognitive and non-cognitive outcomes. An exploration of the mechanisms shows that a larger proportion of repeater peers is associated with reduced after-school study time. The negative effects are driven by male repeaters and are more pronounced among students with less strict parental monitoring at home.
Suggested citation: Xu, Di, Qing Zhang, and Xuehan Zhou. (2019). The Impact of Low-Ability Peers on Cognitive and Non-Cognitive Outcomes: Random Assignment Evidence on the Effects and Operating Channels. (EdWorkingPaper: 19-143). Retrieved from Annenberg Institute at Brown University: http://www.edworkingpapers.com/ai19-143
Di XuUniversity of California Irvine
Qing ZhangUniversity of California Irvine
Xuehan ZhouUniversity of California Irvine
VERSION: October 2019
EdWorkingPaper No. 19-143
1
The Impact of Low-Ability Peers on Cognitive and Non-Cognitive Outcomes:
Random Assignment Evidence on the Effects and Operating Channels
Di Xu (Corresponding Author)
Qing Zhang
Xuehan Zhou1
1 Affiliations: Di Xu (email: [email protected]) is an associate professor of Education Policy and Social Context at the
School of Education, University of California Irvine. Qing Zhang is a doctoral student at the School of Education,
University of California Irvine. Xuehan Zhou is a doctoral student at the School of Education, University of
California Irvine.
Data Availability Statement: The data used in this article can be obtained upon request from the website of
Chinese National Survey Data Archive (http://www.cnsda.org/index.php?r=projects/view&id=72810330).
Disclosure Statement: All the authors of this article declare no conflicts of interest with respect to the research,
authorship, and publication of this article. The authors receive no financial support for the research of this article.
Acknowledgment: The authors are extremely grateful to Rachel Baker, Damon Clark, Greg Duncan, Paco Martorell,
and Jonah Rockoff for their valuable comments and suggestions on this article.
Peer effects are central to understanding the education production function because, if they
exist, the composition and characteristics of peers could potentially affect own behaviors,
preferences, and performance. Yet, the econometric difficulties of estimating peer effects have
been well documented in the literature. Any study that attempts to provide a causal estimate of
peer effects on own outcomes is subject to several methodological challenges including self-
selection into peer groups, the simultaneous influence of peers’ and own outcomes which Manski
(1993) called a “reflection problem,” common shocks that make it difficult to separate the peer
effects from other shared treatment effects, and measurement error that can lead to
overestimation of peer effects in settings without random assignment (Feld and Zölitz 2017).
Ideal data for providing a clean estimate of peer effects therefore would need to contain
orthogonal-to-baseline peer group variation, pre-existing measures that precisely capture peers’
ability and are unlikely to have been affected by own ability, and clear distinction between the
subjects of a peer effects investigation and the peers who provide the mechanism for causal
effects (Angrist 2014).
While the field has started to gather experimental evidence on peer effects in education
settings where students are assigned to peer groups exogenously, the majority of these studies
occurred at the postsecondary education level (e.g., Booij, Leuven, and Oosterbeek 2017;
Carrell, Fullerton, and West 2009; Carrell, Sacerdote, and West 2013; Duflo, Dupas, and Kremer
2011; Lyle 2007; Sacerdote 2001; Zimmerman 2003). In contrast, existing studies that examine
peer effects at the K-12 level typically exploit exogenous between-cohort variations in fixed
student characteristics (such as gender) or prior achievement to identify peer effects (e.g.,
Ammermueller and Pischke 2009; Bifulco, Fletcher, and Ross 2011; Burke and Sass 2013;
3
Carrell and Hoekstra 2010; Carrell, Hoekstra, and Kuka 2018; Gould, Lavy, and Paserman 2009;
Hoxby 2000; Lavy and Schlosser 2011; Lefgren, 2004). One caveat with this approach, however,
is that peer characteristics at the grade or cohort level may only serve as a rough approximation
of the peer interactions at primary and middle schools, since students typically spend more hours
with their classmates and limited hours with their other schoolmates. Additionally, due to data
limitations, there is far less empirical evidence or consensus on the potential mechanisms
through which peer effects operate. Yet, understanding the operating channels of peer effects is
important, as it would inform policies or interventions to optimize the education production
process and outcomes.
This paper provides experimental evidence on peer effects and possible mechanisms in
middle schools by examining whether having low-ability peers, defined as ever being retained
during primary school (referred to as “repeaters” hereafter), has any effect on the cognitive and
non-cognitive outcomes of non-repeater classroom peers. It does so by exploiting a unique
setting where junior high students in China are randomly assigned to classes upon initial school
enrollment. It is important to note that if having low-ability peers indeed impacts a junior high
student’s academic performance and motivation, then these influences occur at a critical juncture
in the life-cycle: an extensive literature indicates that academic choices and career aspirations
based on individual aptitudes, self-concept, and values are formulated during early adolescence
(Eccles, Vida, and Barber 2004; Wang 2013). More importantly, the nine-year compulsory
education ends at grade 9 in China and junior high graduates are then required to choose between
different academic paths which may lead to distinct educational attainment and labor market
outcomes.2
2 Junior high graduates in China are required to choose between a high school that may eventually lead to post-
secondary education, or a vocational school that is oriented towards obtaining occupation-specific skills. Students
4
We begin by documenting the differences between repeaters and non-repeaters in observed
characteristics. Descriptive statistics show that repeaters are not only consistently associated with
lower academic performance relative to non-repeaters, but also are more likely to experience
negative emotions, show lower levels of school engagement, and have lower educational
expectations. These strong correlations motivate the main question of the article: Do higher
proportions of repeaters affect non-repeaters’ cognitive and non-cognitive outcomes? Our
subsequent analyses based on the random assignment design indicate that having greater
proportions of repeaters in the classroom significantly affects non-repeaters’ academic
performance, cognitive assessment score, and school engagement.
Drawing on the rich information included in the survey, we also examine three possible
channels through which peer effects may operate: (i) student perceived student-teacher
interaction at school, (ii) peer relationship and classroom atmosphere, and (iii) daily study hours
after school. Our findings show that reduced study time after school is the most robust and
important channel among the three. We also find that being exposed to a larger proportion of
repeater peers increases a non-repeater’s probability of having a “best friend” who regularly
plays at internet cafés, which has been seen as one of the main causes for school absenteeism and
neglect of daily routine among Chinese teenagers (Reuters 2007). These results provide
suggestive evidence that one of the main channels through which troubled kids negatively affect
their peers is through social networks and joint activities after school.
Taken together, the results from this study make two distinct contributions to the existing
literature on peer effects. First, we provide clean estimates of having repeater peers on own
who choose to attend a high school are also required to choose whether to enter the STEM track or the non-STEM
track. Students cannot easily switch tracks after they make their initial choice because each track prepares students
for a content-specific college entrance exam. Accordingly, students’ academic performance, educational aspirations,
and attitudes toward different subjects formulated in junior high are likely to influence their decisions of academic
paths.
5
outcomes in a unique setting based on a natural experimental design where middle school
students are randomly assigned to classes, and therefore class peers, within a school. A flurry of
studies that are closely related to ours have examined how peers with particularly low academic
ability or high potential of being disruptive may influence own outcomes (e.g., Aizer 2008;
Carrell and Hoekstra 2010; Carrell, Hoekstra, and Kuka 2018; Figlio 2007; Lavy, Paserman, and
Schlosser 2012). This strand of research typically exploits exogenous variations in peer
composition across cohorts and concludes that exposure to low-ability or disruptive peers not
only has negative impact on short-term academic outcomes, but also has long-run educational
and labor market consequences.
We build on this literature but extend it through a research design with several advantages
that make our estimates less susceptible to bias: First, the random assignment of students to
classes purges our estimates of bias from potential confounders associated with peer quality. This
setting also allows us to examine peer effects at the classroom level, which is arguably a better
approximation of peer interactions than at the grade or cohort level. In addition, the status of
being a repeater was determined during primary school, which means that repeaters likely had
limited opportunities to interact with their junior high peers before being labelled repeaters since
they started primary school in different cohorts. Most importantly, Angrist (2014) points out that
peer effects may be biased, even in a randomly assigned setting, due to mechanical relationship
between the measures of own and peer ability. Following his recommendation, our research
design is able to address such mechanical relationship by making a clear distinction between the
subjects of a peer effects investigation (i.e., non-repeaters) and the peers who provide the
mechanism for causal effects (i.e., repeaters).
6
Second, our data include new non-cognitive measures that not only enable us to include
important social-emotional and behavioral measures as key outcomes in addition to academic
performance, but also provide insight into the mechanisms driving the peer effects. Extensive
evidence suggests that non-cognitive measures, such as school engagement and educational
aspirations serve as strong predictors of individuals’ lifelong success even conditional on
academic ability (Borghans et al. 2008; Fredricks, Blumenfeld, and Paris 2004; Moffitt et al.
2011). The data used in our study, the China Education Panel Survey (CEPS), is the first
nationally representative survey for junior high students in China. The CEPS not only includes
student test scores in each subject, but also directly collected information on non-cognitive
measures such as mental stress, school absenteeism, educational expectations, and social and
emotional engagement with the school. Findings regarding these outcomes hence assist
achieving a more comprehensive understanding about peer effects.
Additionally, the CEPS data also include important measures of the educational process, such
as student’s perceived interactions with teachers, student’s perceived classroom environment and
peer relationships, as well as after-school study time. Understanding the impact of repeater peers
on these measures therefore would contribute to the small but emerging literature on the
operating channels of peer effects, which have yielded rather mixed findings (Booij, Leuven, and
Oosterbeek, 2017; Duflo, Dupas, and Kremer 2011; Feld and Zölitz 2017; Lavy, Paserman, and
Schlosser 2012). For example, based on middle school students’ answers to a “school
environment survey” in Israel, Lavy, Paserman, and Schlosser (2012) find evidence for peer
effects on both group functioning and teacher functioning, where a high proportion of low-ability
students negatively influences teachers’ pedagogical practices, raises the level of disruption and
violence within the class, and worsens both student-teacher relationships and inter-student
7
relationships. In the context of Kenyan primary schools, Duflo, Dupas, and Kremer (2011) also
find evidence for classroom ability composition on teacher functioning, where teachers assigned
to a class of high-achieving students display more effort. In contrast, based on data from
university contexts, both Booij, Leuven, and Oosterbeek (2017) and Feld and Zölitz (2017) find
evidence for peer effects on group functioning but no evidence on teacher functioning.
Taken together, these findings indicate that the channels through which peers influence own
outcomes are highly dependent on the specific contexts. Our study builds on the existing
literature and examines peer effects in a new setting. Moreover, in addition to perceived
activities and interpersonal relationships at school, we are able to include after-school study time
as a possible mechanism, which to our knowledge, has never been studied in the previous
literature. Understanding the impact of peers on own behaviors and activities outside of the
classroom is particularly important, as evidence that supports this operating channel would imply
that adolescents may be negatively influenced by troubled peers on a more proactive and
voluntary basis, rather than simply through class time spent together at school.
The rest of the paper proceeds as follows. Section II introduces the specific context of junior
high and grade retention in China. Section III describes the CEPS data and provides descriptive
information about the characteristics of repeaters relative to non-repeaters. Section IV reviews
the methodological challenge in estimating peer effects and presents our methodological
approach in addressing these challenges. Section V presents and discusses our results and
underlying mechanisms of the estimated peer effects. Section VI concludes the paper with a brief
discussion of the interpretation of the findings.
II. Background
A. Compulsory Education in China and Class Assignment
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Education in China is a state-administered system of public education, where the Ministry of
Education standardizes textbooks and curriculum and enforces national education standards. In
an effort to attain a universal education for all school-aged children, the government enacted the
Law on Nine-Year Compulsory Education in 1986, which requires free and universal nine years
of education in the country (six years of primary education and three years of junior high school
education). The local authorities are responsible for following the guidelines formulated by the
central authorities and implementing nine-year compulsory education tailored to local
conditions.
Before the 1990s, all students in primary schools were required to take the junior high school
entrance exam administered either by a district or by individual schools. After that, students were
placed into different junior high schools based on their exam scores. Starting in the mid-1990s,
the Ministry of Education reformed the compulsory education system to promote equal and fair
opportunities for all students and canceled the junior high entrance exam. After graduating from
elementary school (at the end of the sixth grade), students would directly enter into a state-run
junior high school, typically based on the location of students’ Hukou (an official household
registration record that identifies a person’s residency status in an area). According to the
Ministry of Education (2015), in 2014 there are 201,000 primary schools and 52,000 junior high
schools in China. On average 4 primary schools feed into one junior high school. Students can
only attend schools assigned by their Hukou location, which are the schools closest to their
neighborhoods. Since the assigned schools are usually in the vicinity of students’ community, it
is common for students to walk or bike to school both at the primary and junior high level (Li
and Liu 2014). To enforce the policy implementation, the local governments closely monitor the
9
school assignment process and prevent schools from charging extra fees for admitting students
from other districts (Organization for Economic Co-operation and Development 2016).
Partly due to the lack of clear indicators of prior academic achievement, and partly following
the Ministry of Education’s promotion of “equal and fair opportunity for all students,” the
majority of junior high schools in China now follow random assignment of students to classes
upon initial school enrollment, where students are expected to remain within the initial
homeroom class assignment throughout their junior high years (grade 7 through grade 9).3
However, as students move beyond the 7th
grade, teachers and school administrators increasingly
gather knowledge about each student’s behavior and academic performance at school, and are
hence more likely to take actions to improve student outcomes, such as communicating with the
parents, transferring students between classes, or allocating more resources and time to target
lower performing students or students showing problematic behaviors at school. To minimize
possible bias due to teachers’ and schools’ responses to students’ academic performance and
behaviors, we therefore restrict our analyses to schools that randomly assign students to classes
upon initial school enrollment and focus on students in the 7th
grade only, as this is the time
when schools have the least knowledge of students’ academic ability and are least likely to take
additional actions to respond to students’ academic behaviors and performance.
B. Grade Retention in China
Grade retention has been widely used in China as a solution to address insufficient grade-
level achievements (e.g. Chen et al. 2009; Zhang 2014). The formulation and implementation of
3 Junior high schools in China use a homeroom teacher system where students remain in the homeroom class
throughout the school day and subject teachers rotate classes. The homeroom teacher typically teaches one main
subject (English, math, or Chinese); in addition, they also assume the responsibility of looking after the students’
general academic performance in all subjects, personal development, and social activities at school (Chen et al.
2009; Liu and Barnhart 1999; Zhao 2014). Students are usually expected to stay within the same homeroom class
throughout their junior high years though schools may make adjustments from time to time (Chen et al. 2009; Liu
and Barnhart 1999).
10
grade retention policies have been mostly decided by local school administrators following
provincial policy guidelines. Following the Law on Nine-Year Compulsory Education in 1986,
many provinces and municipalities had specific regulations on when a student should be retained
in primary and junior high schools. The criteria to retain students vary across grades, schools,
areas, and provinces. In general, while schools are required to follow provincial policies
regarding grade retention, the specific decision is made primarily at the school level mainly
based on students’ academic performance (Chen et al. 2009). Students are typically retained
when they receive an F in one or more core courses (such as Chinese and math) or in multiple
supplemental subjects (such as PE) (Chen 2013). In Beijing, the capital city of China, for
example, “students in primary schools who fail the annual examinations in either Chinese or
math should take make-up tests; those who fail the make-up tests should be retained. In junior
high schools, students who fail five or more subjects in the annual examinations should be
retained” (Chen 2013, 23).
In 1994, in line with the objectives to promote equal and fair opportunity for all students
regardless of academic merit, the Ministry of Education enacted a policy encouraging school
districts to experiment with the abolishment of retention policy. In the following two decades,
there was a nationwide effort to reduce retention rates (Chen 2013). Yet, the process of
rescinding retention was lengthy and slow. In a 2009 study based on survey and transcript data
drawn from 1,653 students from 36 primary schools in Shannxi province (Chen et al. 2009), one
of the less economically developed provinces in northwest China, more than one third of the
students repeated at least one grade before they entered grade 6.
The cohort of students covered in this study entered junior high school during the fall of
2013. Therefore, the majority of students were in primary school between 2007 and 2013, when
11
the average retention rate was still fairly high in primary schools. Our dataset does not include
information on the specific province the student is in; therefore we were not able to examine the
extent of variation across provinces in the proportion of newly admitted junior high students who
had been retained in primary school. Yet, among all the 112 schools in the national survey data
used in the current study, 92% had at least one grade repeater with an average of 17% repeaters
across all schools, indicating that grade retention in primary schools was still a fairly common
phenomenon for the cohort of students examined.
III. Data
A. China Education Panel Survey
The China Education Panel Survey (CEPS) is the first nationally representative survey for
junior high students in China. The primary analyses of this study are based on data from the
baseline wave that was collected during the spring of the 2013–2014 academic year. The CEPS
employs a stratified, multistage sampling scheme. In the first stage, 28 counties/districts were
chosen from 2,870 counties/districts. Four schools from each county/district were selected and
two classrooms were then randomly selected from 7th grade and another two from 9th grade in
each sample school.4 Finally, all students from these selected classrooms were surveyed,
resulting in a sample of approximately 20,000 students in 438 classrooms of 112 schools.
The CEPS administered five separate questionnaires to the i) sample students, ii) homeroom
teachers, iii) subject teachers for the three main subjects (Chinese, English, and math), iv)
students’ parents, and v) school administrators. Hao and Yu (2015) provide a comprehensive
summary of CEPS in their recent report; here we briefly review the features of the baseline
survey most relevant for our analysis. The school administrator questionnaire solicited
information about school resources, school management, and other school-level statistics about
4 If the sample schools had only 1 or 2 classes in each grade, all classes were included in the sample.
12
teachers and students. One important question asked in the school administrator questionnaire is
whether the school randomly assigns students to different classrooms. Among all the 112 schools
sampled, 83% (N=93) reported that students were randomly assigned to classrooms upon entry
into the junior high school; the homeroom teacher and main subject teachers were then randomly
assigned to each class. In the methodology section, we present statistical evidence to show that
students in the 7th
grade in these schools indeed seem to be randomly assigned to classes, as
indicated by preexisting student demographic and family characteristics. The teacher
questionnaire collected information from each homeroom and main subject teacher on teachers’
demographic characteristics, subject taught, and teaching experience. Finally, the student
questionnaire collected information about student demographic and family background
characteristics, cognitive measures such as academic performance in each of the three main
subjects (Chinese, English, and math), as well as non-cognitive measures such as students’
perceived interaction with teachers of the three main subjects, perceived classroom climate,
experience of negative emotions, school disengagement, and educational expectations. In the
following section, we explain in more detail the outcome and control variables used in this study
and how they are constructed.
B. Key Measures and Variable Definitions
We focus on five domains of student outcomes: academic performance, cognitive
assessment, mental stress, school disengagement, and educational expectations.5 Following
Kling, Liebman, and Katz (2007) and Deming (2009), we create summary indices for domains
5 We use principal factor analysis to group our non-cognitive measures into three domains (i.e., mental stress, school
disengagement, and educational expectations) following Gong, Lu, and Song (2018). A detailed description of the
procedure can be found in Appendix 1.
13
that contain multiple survey items.6 The aggregation can partly address the problem of multiple
hypothesis testing by reducing the number of outcome measures; it also has the potential to
increase the statistical power to detect effects that go in the same direction within each domain
(Kling, Liebman, and Katz 2007). Specifically, we first normalize each component of a domain
to have a mean of zero and a standard deviation of one for all non-repeaters at the school level.
We then take the equally weighted average of the z-scores of the components with equalized
signs so that larger values of the index represent higher levels in that domain. We describe each
summary index and the specific survey items used to construct them below. It is worth noting
that since we focus on the 7th
grade (or the 1st grade of junior high school), students in our
analytical sample would have spent almost one year with their classmates at the time of the
survey.
Academic performance. Students are required to report their most recent midterm test
score for each of the three main subjects: Chinese, English, and math. Within a grade at a school,
teachers who teach the same subject use the same syllabus; the mid-term and final exams are
administered by school and are common across all students in a grade. Student test scores are
therefore comparable within a particular grade at each school. The raw score is on a 150-point
scale.
Cognitive assessment. CEPS also required all the participating schools to administer a 15-
minute standardized cognitive ability test. The cognitive ability test assesses a student’s aptitude
on reasoning and problem-solving in three dimensions: (i) language, (ii) vision and space, and
(iii) arithmetic and logic.7 The test follows similar practices used in a number of cognitive tests
6 For all of our main findings, we also present the estimates for specific survey items that measure student outcomes
in each domain (rather than summary indices) in Appendix Table 2. 7 Specifically, the language dimension assesses verbal analogy and verbal reasoning. The vision and space
dimension examines geometric pattern recognition, a paper-folding test, and application of geometric graphs. The
14
conducted in other countries, such as the Taiwan Education Panel Survey and the National
Education Panel Study in Germany (Zhao et al. 2017).
In addition to the two cognitive outcome measures, we also examine three domains of non-
cognitive outcomes. Specifically, mental stress was measured by five survey items, asking
whether the respondent has ever experienced feelings such as feeling down, depressed, unhappy,
not enjoying life, or sad in the past seven days, which was based on a well-established clinical
depression assessment using a five-point Likert scale (Löwe, Kroenke, and Gräfe 2005) ranging
from 1 (Never) to 5 (Always). Higher values thus indicate that students experienced more
negative feelings, and therefore, higher levels of mental stress.
School disengagement. School disengagement was measured by six survey questions: “I am
often late for school”, “I am often absent from school”, “I seldom participate in school or class
activities”, “I do not feel close to people at this school”, “I feel bored at school,” and “I want to
attend another school.” All the questions about school disengagement were measured on a 4-
point scale ranging from 1 (strongly disagree) to 4 (strongly agree), with higher scores indicating
higher levels of school disengagement.
Educational expectations. Student educational expectations were measured through questions
about the highest level of education the student expected to receive and the confidence level a
student has about his or her future. For the highest level of education, it was measured by ten
options ranging from “Drop out now” to “Get a doctoral degree.” We code this variable as
expected years of education for the purpose of our analysis.8 For a student’s confidence level
arithmetic and logic dimension assesses applied problem solving, replacement of expressions by self-defined
symbols, number sequence completion, numerical pattern recognition, probability, and quantitative comparison and
reverse thinking. 8 Specifically, we recode this variable to the student’s expected years of schooling based on the normal time to
degree in China: 7 years of education for students who chose “dropping out now” or “does not matter”; 9 years of
education for “junior high school”; 12 years of education for “technical secondary school,” “vocational high
school,” or “senior high school degree”; 15 years for “junior college degree”; 16 years for “bachelor’s degree”; 18
15
about his or her future, the response format consisted of a 4-point scale, ranging from 1(not
confident at all) to 4 (very confident). We first standardize each item and then create an index
variable of “educational expectations” by taking the average score of the two items.
Student, Teacher, and Classroom Control Variables. Control variables include information
collected at the student level, teacher level, and classroom level. Specifically, student
background characteristics include gender, whether the student lives in a rural or urban hukou,
whether the student is the only child in the household, age, parents’ education level, family
income, and potential family risk factors (i.e., parental absence, whether the father drinks
regularly, and whether parents always quarrel with each other). Teacher background information
was collected through individual teacher surveys, which include information on their
demographic characteristics (i.e., gender and age), whether he/she graduated from a normal
institution versus a comprehensive university, whether he/she has a teaching certificate, highest
level of education, any prior teaching awards, teaching title, and years of teaching experience.
Summary statistics of teacher background characteristics are presented in Appendix Table 3.
Finally, since all the students in a sample class were surveyed, we are also able to calculate the
average classroom characteristics and include them as control variables in the analysis, including
class size, percentage of boys, percentage of low-income families, and percentage of students
with at least one family risk factor.
C. Summary Statistics
For the purpose of our analysis, we restrict the analytical sample to the 7th
graders in 93
schools (out of the 112 schools in the full sample) that use a random algorithm to assign students
years for “master’s degree”; and 21 years for “doctoral degree.”
16
and teachers to classes, resulting in a sample of 8,520 students.9 Appendix Table 4 compares the
characteristics of schools that claimed to use random assignment and those that did not. It seems
that schools that did not claim to use random assignment are more likely to be located in rural
regions and have a teacher force that is older in age than the schools that claimed to use random
assignment. We further drop 66 students who have missing information on grade retention
status.10
The final sample consists of 1,392 repeaters and 7,062 non-repeaters.
The missing rates for the outcome and mechanism measures among non-repeaters are
generally low, ranging between 1% and 4%. To examine whether students with certain
characteristics are more likely to answer the survey, we run OLS regressions that correlate
student characteristics and whether a student has a missing value for a specific outcome measure,
controlling for school fixed effects. Appendix Table 5 shows the missing patterns for various
domains of outcome variables.11
Overall, except for a handful of cases, student characteristics do
not seem to be consistently correlated with a student’s probability of answering a survey
question. In addition, results in Appendix Table 5 also show small and insignificant correlations
between our key treatment variable (proportion of repeater peers) and non-repeaters’ probability
of responding to each outcome measure. Finally, for students who are missing information on
other covariates, we retain them in the analytical sample and include indicators for missing data
on those variables.
9 As mentioned previously, we focus on 7th graders only due to the concern that there might be non-random
between-class mobility in later years of junior high school. 10
Among the 66 students who have missing information on grade retention status, the majority (87%) are male
students; about half are from urban families and 14% are from low-income families. The average age of the 66
students is 14 years old. 11
To save space, we only present the results on the variable that is subject to the largest missing rate from each
domain of the outcome and mechanism measures. For example, the variable “not enjoying life” has the largest
missing rate among the outcome measures under the domain of “Mental stress”. The missing rate across all variables
is low nevertheless: less than a 4% missing rate for covariates with missing values.
17
On average, approximately 16% of the 7th
graders were ever retained in primary school.
Among these students, the majority (80%) were retained only once. The first column in Table 1
shows the demographic and family characteristics for all students while columns 2 and 3 present
descriptive information for repeaters and non-repeaters respectively. Overall, the comparison
between the two groups indicates that the repeaters are more likely to be older in age, have
siblings, live in a rural hukou, have parents with lower levels of education, and be from families
with lower income. It also appears that repeaters are more likely to be subject to potential family
problems, such as having fathers who drink regularly and parents who fight with each other more
often. Yet, these descriptive patterns might be partly due to between-school differences in the
share of repeaters. For example, if repeaters are more likely to concentrate in certain types of
schools, the raw difference between repeaters and non-repeaters could thus partly reflect
between-school distinctions in student characteristics.12
To address between-school variations in
the share of repeaters and student characteristics, column 4 of Table 1 further presents the
average difference between repeaters and non-repeaters within the same school. The results
generally echo the patterns shown in column 2 and column 3, where repeaters are more likely to
live in a rural hukou, have siblings, be older, and have fathers with drinking problems.
Table 2 presents descriptive information on each outcome measure. The first two columns
summarize student mean scores for repeaters and non-repeaters respectively; column 3 presents
the gaps between the two groups, adjusting for school fixed effects to take into account overall
variations in student outcomes across schools. Finally, column 4 shows the number of non-
repeaters with non-missing values for each outcome measure examined. Unsurprisingly,
12
We directly examine whether the share of repeaters at a school is associated with available school characteristics
and the results are presented in Appendix Table 6. Most of the coefficients are small and nonsignificant with two
exceptions: repeaters seem to be more concentrated at schools that enroll a higher proportion of low-income families
and also schools with smaller enrollment size.
18
repeaters are associated with consistently lower test scores relative to non-repeaters across all
subject areas. The average raw test score among repeaters is 69 on a 150-point scale, versus 80
among non-repeaters. When compared within schools, repeaters still score 5.5 points lower on
average than non-repeaters. The cognitive assessment score for repeaters is also significantly
lower than that of non-repeaters even after we compare the students within the same school.
Results from Table 1 seem to suggest that repeaters are more likely to be from higher risk
families, which may not only result in lower academic ability, but may also induce psychological
and behavioral problems that could influence class peers. To shed light on this possibility, Table
2 further presents students’ non-cognitive outcomes in junior high, including their mental stress,
school disengagement, expected years of education, and confidence about future.13
Indeed, it is
immediately apparent that repeaters are substantially more likely to experience negative
emotions, show higher levels of mental stress, be less engaged behaviorally and emotionally in
school, and have fewer expected years of education and lower confidence about the future. Such
differences remain within schools.14
Taken together, the descriptive statistics seems to suggest
that repeaters are not only low academic achievers but may also have other social-emotional or
behavioral problems that may be associated with negative externalities for their peer classmates.
IV. Methodology
A. Validity of the Random Assignment
13
It is important to note that since “expected years of education” and “confidence about future” are measured in
different scales, we show the descriptive statistics for the raw score of each variable separately. In all of the
subsequent regression analyses, we combine them into a summary index by first standardizing each item and then
taking the average score of the two. We also present the estimates on the two measures separately instead of the
summary index in Appendix Table 2. 14
It is worth noting that these outcome measures may also partly reflect the impact of the “repeater” status on
repeaters’ academic and emotional outcomes during the first year in junior high. For example, some researchers
suggest that retained students, being older than the majority of their classmates, may feel less attached to school
(Jimmerson 2001). However, studies examining the impacts of retention on students’ academic performance and
motivation have led to inconsistent results, and among those that report negative effects of retention on student
outcomes, the effect sizes are generally small (for meta-analytic reviews, see Allen et al. 2009 and Jimmerson 2001).
Therefore, the large gap between repeaters and non-repeaters in their cognitive and non-cognitive outcomes should
at least partially capture the pre-enrollment differences between these two groups.
19
The validity of the causal inferences that follow rests on the successful randomization of
students to classes. While the institutional setting we study makes it clear whether or not
administrators in the schools follow random assignment upon students’ initial school enrollment,
we cannot rule out the possibility that in some cases students were lobbied to be placed in a class
with a better teacher or better peers. For example, influential parents might pull their children out
of a class with a particularly high proportion of repeaters. This problem is less of a concern in
this particular context, considering that four primary schools feed into one junior high school on
average and therefore it is unlikely that parents would know all the repeaters in the feeding
primary schools and manage to avoid them. Additionally, restricting the sample to 7th graders
only also helps reduce the extent of the problem, since it is at the beginning of the junior high
years when parents and teachers have the least knowledge about each student’s academic ability.
However, we cannot rule out the possibility that teachers and parents may still gather such
information through various channels. Below we evaluate the validity of the randomization
formally to provide empirical evidence for our identification.15
To assess whether the student randomization protocol was implemented as designed, we test
for balance in predetermined student family background characteristics, examining whether the
background characteristics of a non-repeater, such as parental education and occupation, are
correlated with the proportion of repeater peers he/she is assigned to after conditioning on school
fixed effects. It is worth noting that although the CEPS survey was conducted after the students
in our sample had enrolled in a junior high school and therefore the family and parental
15
Additionally, in one of our robustness checks, we further use one question in the school administrator
questionnaire to identify schools in our sample that might violate the random assignment due to pressure from
parents. Specifically, this question asked the school administrators whether parents made special requests to assign
students to certain classrooms, on a scale of 1 (not true at all) to 4 (true). Among the 93 schools that indicated using
random assignment, only 16 school administrators answered true (4) or somewhat true (3) to this question. We thus
conducted a robustness check of all of our analyses (including main outcomes and mechanisms) excluding the 16
schools. Results are presented in Appendix Table 7 and are fairly consistent with our main findings.
20
background characteristics are not measured prior to random assignment, the background
characteristics (such as parents’ educational level) are unlikely to be impacted by the child’s
class assignment in junior high.
We first establish that these family and parental characteristics are in fact strong predictors of
the key outcome measures. In columns 1 to 5 of Table 3a, we regress non-repeaters’ outcomes on
all available student family background characteristics, controlling for school fixed effects. The
results indicate that several demographic and family characteristics, such as gender, age, parental
education level, family income, and parental occupation, are highly significant predictors of
student cognitive and non-cognitive outcomes.
Having identified a set of baseline characteristics that predict key outcome measures, we
evaluate randomization of students into the treatment by regressing the proportion of repeater
peers in a class which a non-repeater is assigned to on that non-repeater’s demographic and
family characteristics. In calculating the proportion of repeater peers, we divide the total number
of repeater students in a class by the total number of students in that class minus one. If students
are indeed randomly assigned to classes within a school then, once conditional on school fixed
effects, there should be no systematic association between student characteristics and assignment
to proportion of repeaters as peers. The results shown in column 6 of Table 3a indicate that
overall these predetermined variables do not seem to systematically predict the likelihood that a
student is assigned to a class with higher proportions of repeaters. An F test for the joint
significance of all the predetermined demographic and family characteristics is also insignificant,
providing support for the validity of the randomization.
Another way to examine the validity of the randomization is to correlate the proportion of
repeater peers a non-repeater is assigned to with the non-repeater’s predicted outcomes using
21
available demographic characteristics. If the randomization is indeed successfully implemented,
we should expect no correlation between the predicted outcomes and proportions of repeaters
assigned. We use cognitive outcomes for this additional check because they are less noisy than
non-cognitive measures and are more likely to detect possible correlation, if there is any.
Specifically, we first predict the four cognitive outcomes (i.e., Chinese, math, and English
midterm test scores and cognitive assessment scores) of non-repeaters by regressing these
variables on all the available observables listed in Table 3a. We then regress the fitted value of
cognitive outcomes on the proportion of repeater peers. Results presented in Appendix Table 8
and Appendix Figure 1 indicate that there is no significant correlation between the predicted
outcomes of non-repeaters and the proportion of repeater peers they are assigned to, except for
English scores, where we identify a small correlation that is marginally significant at the 0.1
level.
Even though students are randomly assigned to classes, one potential threat to our
identification strategy is that schools might assign teachers in a systematic way. For example, a
school might assign more experienced homeroom teachers to classes that have more students
with behavioral problems. Although this is less likely to happen given that we are focusing on
the first year of junior high when schools have minimal information on students’ academic
ability and behaviors, we conduct two balance tests at the class level to explore the extent of the
problem more formally. The first one examines possible correlation between the proportions of
repeaters and teacher assignment. Specifically, we regress the proportion of repeaters in a class
on the characteristics of the homeroom teacher assigned to that class. Results in Table 3b
indicate that, once controlling for school fixed effects, there is no systematic correlation between
the characteristics of the homeroom teacher and the proportions of repeaters in that class. In
22
addition, we also examine the correlation between the average characteristics of students in a
class and key characteristics of the homeroom teacher assigned to that class, where we use
students’ background characteristics aggregated at the class level to predict homeroom teachers’
gender, age, whether having a college degree or higher, and teaching experience. The results are
presented in Appendix Table 9 and further support the validity of randomization, where none of
the teacher characteristics is systematically correlated with the average characteristics of the
students in a class.
B. Econometric Specification for Student-Level Analysis
Having validated the randomization fidelity, our empirical model writes as follows:
(1) Yigs =
, where Yigs is an outcome such as cognitive assessment score for non-repeater student i randomly
assigned to class g at school s. The variable is the proportion of repeater peers for
a non-repeater in that particular class, which is calculated by dividing the number of repeaters by
the total number of students in that class minus one. For easier interpretation, we standardize our
outcome measures and multiply the proportion of repeater peers by 100 (such as converting 2%
to 2). hence measures the estimated effect on the outcome measure in standard deviations
given one percentage point increase in the proportion of classroom repeater peers.
is a vector of individual background characteristics listed in Table 1.
further controls for the characteristics of the homeroom teacher assigned to
23
this class listed in Table 3b. is a vector of classroom average peer
characteristics such as percentage of boys and percentage of low-income students. represents
the school fixed effects.
One concern with the school fixed effects model is that only schools with between-class
variations in proportion of repeaters would contribute to the estimate of . Figure 1 shows the
distribution of proportion of repeaters across all classes in our analytical sample. Among all the
93 schools in our analytical sample, there are substantial variations in the proportion of repeaters,
ranging from 0% to 65.5%. Since our identification draws on the between-class variations in
proportion of repeaters within a school, Figure 2a further pairs the two classrooms in each school
and creates a scatter plot, where each dot represents a school, with the share of repeaters in
classroom 1 on the x-axis and the share of repeaters in classroom 2 (of the same school) on the y-
axis. The results indicate that while there are strong correlations in the proportion of repeaters
between each pair of classes within a school, very few of the schools fall exactly on the 45°
diagonal line, indicating that most of the schools have variations in the share of repeaters
between classrooms.16
Figure 2b further shows the distribution of within-school between-classroom differences
in the share of repeaters. Among all the 93 schools in our analytical sample that specifically
indicated using a random algorithm to assign students to classes, 3 schools only had one class.
Among the rest of the 90 schools, 81 (or 87%) have between-class variations within school in the
proportion of repeaters, with an average within-school variation of 5.51 percentage points and a
16
While schools without variation in the proportion of repeaters will not contribute to the estimate of the peer
effects, these observations can still contribute to the estimation of other coefficients and are thus retained in our
analysis. Standard errors are clustered at the school level to accommodate correlations among students as well as
between classes within the same school. In our robustness checks, we also cluster the standard errors at the class
level; the results indicate that the school-level clustering generates the largest standard errors and therefore represent
more conservative estimates.
24
median of 3.65 percentage points, therefore providing sufficient within-school variation to
support our analyses. Additionally, while the within-school between-class difference in
proportions of repeaters ranges between 0% and 26%, the vast majority (83%) have a within-
school variation less than 10%, indicating that the estimated effects are unlikely to be primarily
driven by a small set of schools that have a larger variation in peer composition.17
C. First Difference at the School Level
In addition to the student-level analysis, we also aggregate the data at the class level and run
all the analyses first differenced at the school level. Since each school includes two classes and
since randomization occurred at the school level, these first-differenced estimates are a
straightforward variation of the matched-pairs design that provides a conservative robustness
check for the analyses conducted at the student level. More specifically, we relate first
differences in average outcome of non-repeaters against first differences in the proportions of
repeaters:
(2) ( ̅ - ̅ ) = ̅ ̅
where ̅ and ̅ represent the average outcomes of non-repeaters in class 1 and class 2 at
school s respectively; are the proportion of repeaters in the
corresponding class; is the average background characteristics of the non-repeaters in a
17
To further rule out the possibility that schools with particular characteristics may be more likely to have a larger
variation in peer composition and therefore drive the estimated effects, we directly examine the correlation between
within-school variation in the share of repeaters and a set of school characteristics, including school size, average
class size, proportion of students with rural Hukou, average parental education, whether the school is located in rural
areas, school funding per student in the current year, and proportion of students from low-income families. Results
from this correlation analysis are presented in Appendix Table 10 and indicate that within-school variation in the
share of repeaters is not associated with any of the school characteristics mentioned above, therefore providing
additional support that the estimated effects are unlikely to be driven by particular types of schools.
25
particular class and T is a vector of the characteristics of the homeroom teacher assigned to a
class. Among all the 93 schools that used random assignment of students to classes, three schools
only had one class, therefore providing us with 90 observations for the first-difference
estimation. All the first-difference analyses using equation (2) are weighted by class size.
V. Results
A. Main Effects
We begin by plotting the aggregate distributions of the average outcomes of non-repeaters
against proportions of repeaters, first differenced at the school level. Figure 3 visually shows the
correlations in terms of all the five outcome indices. First of all, there are noticeable negative
correlations between proportions of repeaters in a class and both cognitive outcome measures of
non-repeater classmates (academic performance and cognitive assessment score). There also
seems to be a negative but less pronounced correlation between proportions of repeater peers and
educational expectations, and slightly positive correlations between proportions of repeater peers
and non-repeaters’ level of mental stress and school disengagement.
Table 4 quantifies these correlations based on five different model specifications. We start
with a model that only controls for school fixed effects (Column 1) and then progressively add
the controls for individual (i.e., non-repeaters’) (Column 2), homeroom teacher (Column 3), and
classroom average peer characteristics (Column 4). Finally, column 5 presents the first-
difference estimates at the school level based on equation (2).
The estimates echo the patterns shown in Figure 3. Even in the most highly specified model
that controls for school fixed effects with the full set of controls (Table 4, column 4), exposure to
higher proportions of repeater peers is associated with a significant decrease in non-repeaters’
academic performance and cognitive assessment score. Specifically, one percentage point
26
increase in the proportion of repeater peers decreases academic performance by almost 2.1% of a
standard deviation (SD) among non-repeaters. In other words, adding one more repeater to a
class of 46 (which is the average class size in our analytical sample; roughly a 10% standard
deviation increase, or an increase in the proportion of repeater peers by 2 percentage points) is
associated with a decline in average academic performance for non-repeaters in that class by
4.2% of a standard deviation toward the end of the 7th
grade. Similar magnitude of the negative
effects is also observed for cognitive assessment score (by 2.3% of one SD). Column 5 presents
the first-difference estimates aggregated at the school level. Even with this relatively more
conservative approach with substantially larger standard errors, the negative correlations
between proportions of repeater peers and non-repeaters’ academic performance and cognitive
assessment scores remain significant. Appendix Table 2 also shows the estimated impacts of
proportions of repeaters on the values measured by each single survey item instead of the
summary indices, and the sizes of the effects on the test scores of the three subject areas are
strikingly consistent.
In terms of non-cognitive outcomes, student-level analyses controlling for school fixed
effects (column 1) indicate that exposure to a higher proportion of repeaters negatively
influences non-repeaters’ mental health, school engagement, and educational expectations.
However, only the impact on school disengagement remains significant when we further control
for individual, homeroom teacher, and classroom average peer characteristics (column 4), or in
the first-difference analysis at the school level (column 5).
One potential concern regarding our analyses is that as we test more and more outcomes, the
problem of false positives could arise from multiple hypothesis testing, where even a randomized
experiment could yield some p-values that appear to be statistically significant purely by chance
27
if a sufficient number of hypotheses are tested. We have partly addressed this concern by
aggregating outcome measures within the same domain and creating summary indices following
previous studies (e.g., Anderson 2008; Deming 2009; Kling, Liebman, and Katz 2007). Another
approach that has been commonly used in the existing literature to address the multiple
hypothesis testing problem is to adjust the p-values controlling for the familywise error rate – the
probability of rejecting at least one true null hypothesis – using the stepwise resampling method
(e.g., Anderson 2008; Kling, Liebman, and Katz 2007; Romano and Wolf 2016). We therefore
follow the procedures described in Romano and Wolf (2016) to jointly test the null hypothesis
that there is no treatment effect on any of the outcomes or mechanisms. The adjusted p-values
presented in Appendix Table 11 indicate that the significant effects of having repeater peers on
academic performance, cognitive assessment, and school disengagement are unlikely to be an
artifact of multiple hypothesis testing.
B. Possible Mechanisms
Having found that repeater classmates impose significant externalities on classroom peers,
which are particularly robust in terms of academic performance, we further explore possible
channels driving these effects. Specifically, we draw on students’ responses to several survey
items to shed light on three possible mechanisms in this particular research context: student-
teacher interaction, student-student classroom interaction, and study hours after school.
Student-teacher interaction is measured by eight survey items on non-repeaters’ perceived
interaction with their homeroom and subject teachers teaching any of the three main subject
areas – Chinese, English, and math. Students were first asked about their interactions with each
of the three subject teachers, including whether the subject teacher asked the students to answer
questions in class frequently and whether the student felt that the teacher praised him/her
28
frequently. Two additional questions asked about students’ interaction with their homeroom
teacher, including whether the student felt criticized by the homeroom teacher frequently and
whether the student felt praised by the homeroom teacher frequently. All the questions are based
on a 4-point scale ranging from 1 (strongly disagree) to 4 (strongly agree).18
If teachers indeed
adjust their expectations of students and behaviors based on classroom peer composition, we
would expect that having a greater proportion of repeaters in a class influences how teachers
interact with non-repeaters. For student-student interaction, students were asked to respond to
two statements, “most of my classmates are nice to me” and “my class has a good atmosphere.”
Both questions were answered in a 4-point scale ranging from 1 (strongly disagree) to 4 (strongly
agree). Finally, students were asked to report their time spent on study after school (in hours),
which includes study time on school work, tutoring, and assignments from tutoring. We create a
summary index for both student-teacher interaction and student-student interaction following the
same procedures for creating the summary indices for our outcome measures. We also
standardize students’ self-reported study hours for easier interpretation.
The first two columns in Table 5 show the mean and standard deviation of repeaters and
non-repeaters separately for each index. On average, non-repeaters report higher values for
student-teacher interaction, student-student interaction, and more time spent on study after
school. Columns 3-5 present the estimated effects of repeater peers on these measures, starting
with a school fixed effect regression and progressively adding individual, homeroom teacher,
and classroom average peer controls. The results suggest that proportion of repeater peers in a
class is not significantly associated with non-repeaters’ perceived interaction with their
18
We reverse code the item that asked about students’ perception of criticism by the homeroom teacher when we
aggregate the eight items into a single measure, so that higher values indicate stronger and more positive interactions
between the student and the teacher.
29
teachers.19
However, a greater proportion of repeater peers is negatively associated with non-
repeaters’ perceived peer relationships. Specifically, a one percentage point increase in the
proportion of repeater peers leads to approximately 1% of a one standard deviation decrease in
students’ evaluation of classroom peer interaction. In other words, adding one more repeater to a
class of 46 is associated with a decline in non-repeaters’ perceived classroom peer interaction by
2% of one standard deviation (2*0.010=0.020). Yet, the estimated effect becomes insignificant
once we further control for available characteristics of the homeroom teacher and classroom
average peer characteristics in columns 4 and 5.
The third row of Table 5 presents the impact of having a larger proportion of repeater peers
on non-repeaters’ daily hours spent on study after school. The results indicate that having a
greater proportion of repeater classmates significantly reduces non-repeaters’ after-school study
time. One percentage-point increase in the proportion of repeater peers is associated with a
significant reduction in after-school study hours by approximately 1% of a standard deviation. In
other words, adding one more grade repeater to a class of 46 is associated with an average
decline in non-repeaters’ self-reported after-school study time by approximately 1.2 minutes
daily (2*0.01*60=1.2). The association between repeater peers and self-study hours remains
significant in models that further control for homeroom teacher and classroom average peer
characteristics. Although the effect size seems small for each student, it adds up to a total of
almost one less hour of study time on a daily basis for an average class of 46 students.
To sum up, we find some suggestive evidence for peer effects on inter-student relationships
but do not find evidence for student-teacher interactions. More interestingly, after-school study
hours seem to be the most robust of the three discussed channels in our setting. This finding
19
We also separately examine students’ perceived interaction with subject teachers and homeroom teachers; none of
the analyses yield significant estimates.
30
suggests that peers may influence own academic efforts by influencing the student’s time
investments after school. One possibility is that having low-ability peers may induce non-
repeaters to be more relaxed and thus exert less effort after school. However, perhaps a more
compelling channel is that repeaters may spend time together with non-repeater classmates and
thus repeaters, who tend to spend less time on study on average as shown in Table 5, could
influence their non-repeater friends’ after-school activities and time use through group activities
and peer pressure.
To further shed light on the specific channel of after-school activities, we examine the
association between proportion of repeater classmates and a non-repeater’s probability of having
friends who play at internet cafés regularly. According to a recent study on internet addiction
using a nationally representative sample of Chinese primary and middle school students, surfing
and playing video games in internet cafés has become the most important risk factor leading to
internet addiction among teenagers (Li et al. 2014). By 2016, there were more than 140,000
internet cafés in China (Zhiyan Consulting Group, 2016), which have been seen as one of the
main reasons for school absenteeism, neglect of studies, and “hotbeds of juvenile crime” among
Chinese teenagers (Reuters 2007). Although CEPS does not include information on individual’s
own time spent in internet cafés, students were asked whether any of their top five best friends
play at internet cafés regularly. Since peer influence is an important factor in internet and digital
game addictions (e.g., Gunuc 2016), understanding the impact of repeater peers on one’s
probability of having friends with risk behaviors could shed light on why exposure to greater
proportions of repeater classmates may negatively influence one’s study time after school. In
addition to having friends who play at internet cafés regularly, students were also asked whether
any of their top five best friends ever had other behavioral problems, including skipping classes,
31
violating school rules, fighting, drinking, and smoking. We aggregated the information and
created a variable to indicate whether any of a student’s top five best friends has general
disciplinary problems.20
Results presented in the last two rows of Table 5 indicate that having repeater classmates is
not significantly associated with non-repeaters’ probability of having friends with general
disciplinary problems. Yet, having a greater proportion of repeater peers increases a non-
repeater’s probability of having a friend who regularly plays at internet cafés after school. Based
on the model specification with school fixed effects, individual characteristics, and homeroom
teacher characteristics (column 4), a one percentage point increase in repeater peers is associated
with an increased probability of having friends who regularly goes to internet cafés by 0.3
percentage points. These results provide suggestive evidence that the negative impacts of
repeaters on their non-repeater classmates may operate through social networks and joint
activities after school. Yet, the estimated effect becomes insignificant once we further control for
classroom average peer characteristics in column 5.
C. Heterogeneous Effects by Parental Monitoring and Mother Education
Having found that repeater classmates impose significant externalities on non-repeaters on
average, we further explore whether there is any evidence that such spillovers are heterogeneous
by the characteristics of non-repeaters. In particular, given the extensive evidence on the impact
of parental involvement on students’ academic outcomes, the negative externalities of repeater
peers might be mitigated if a student has parents who regularly check his homework and monitor
his behaviors after school, whereas students with less involved parents and less strict discipline
20
Among students who had friends with disciplinary problems, the majority only had one such friend. In a separate
robustness check, we also code the variable as the number of best friends regularly going to internet cafés or
showing general disciplinary misbehaviors instead. The results are almost identical.
32
at home might be more vulnerable to having repeater friends, particularly given that one of the
most important mechanisms seems to be reduced study time after school.
To explore this possibility, we construct two measures as proxies of parental involvement in
monitoring their children’s academic and after-school activities based on survey questions from
the parents’ questionnaire: (1) a composite score of child disciplinary practices at home that
consists of eight specific questions regarding various activities,21
and (2) a survey question that
asked whether the parents check their child’s homework regularly at home. Panel A of Table 6
presents the heterogeneous effects of repeater peers on non-repeaters’ cognitive and non-
cognitive outcomes. Results show that repeaters’ negative spillovers on academic performance,
cognitive assessment score, and school disengagement seem to be stronger among students who
are from families without strict child discipline at home (Column 1), although none of these
differences reach statistical significance (Column 3). We observe similar patterns of results when
we divide the sample by whether the parents check their child’s homework regularly. Results
presented in Columns 4 and 5 show that having a larger proportion of repeater peers affects
students from families without regular homework checking more severely on cognitive
assessment score and school engagement compared to students whose parents check their
homework regularly. Finally, given the ample evidence that establishes the connection between
mother’s education and children’s cognitive and social development (e.g., Menaghan and Parcel
1991; Parcel and Menaghan 1994) and delinquency (Hillman, Sawilowsky, and Becker 1993;
McCord 1991), we further examine whether the negative effects of repeaters are moderated by
mothers’ education level, where we divide the sample in half by mothers with “a college degree
21
The eight questions asked parents whether they have strict rules regarding their child’s (1) academic test scores,
(2) behaviors and activities at school, (3) going to school on time every day, (4) going back home on time every day,
(5) rules about choosing the right friends, (6) dress code, (7) time spent on internet, and (8) time spent on watching
TV.
33
or higher” versus mothers with “a high school degree or less.” Results show that the negative
spillovers of repeaters on academic performance and cognitive assessment score are primarily
driven by students whose mothers have below-college education (Panel A, Column 8). For these
students, a one percentage increase in the proportion of repeaters in their class leads to 2.2% of a
standard deviation decrease in their academic performance and 2.4% of a standard deviation
decrease in their cognitive assessment score toward the end of the 7th
grade. In contrast, the size
of the coefficients on students whose mothers have a college education is substantially smaller
and no longer significant.
Taken together, the results from the heterogeneity analyses presented in Panel A of Table
6 indicate that the negative effects of having repeater peers seem to be more pronounced among
non-repeaters from families with less strict parental monitoring. Among students from these
families, academic performance and cognitive assessment score are the areas that are most
severely and persistently affected by having a larger proportion of repeater peers. One possible
explanation for the heterogeneous impact is that students from families without strict parental
monitoring are more likely to interact with disruptive peers and therefore reduce their daily study
time after school.
Panel B of Table 6 empirically explores this possibility by examining the heterogeneous
effects of repeater peers on available mechanism measures. Indeed, while we do not find any
heterogeneous effects on non-repeaters’ in-school activities (such as student-teacher interaction
and student-student interaction), we find fairly consistent patterns that repeater peers have a
noticeably larger impact on daily after-school study time and probability of having friends who
go to internet cafés among non-repeaters from families that lack strict child discipline at home,
do not regularly check homework, or have less educated mothers. For example, among students
34
from families without strict child discipline at home (column 1), a one percentage point increase
in the proportion of repeater peers is associated with a significant reduction in daily after-school
study hours by approximately 2.5% of a standard deviation.22
D. Male Repeaters vs. Female Repeaters
Finally, we explore whether the spillover effects depend on the gender of the repeaters, based
on two considerations. First, ample research has shown that male teenagers are associated with
higher levels of disciplinary and misbehavior problems than girls (Mendez and Knoff 2003). For
example, boys are more likely to show personal and physical aggression than girls (McGee et al.
1992; Zoccolillo 1993). Indeed, descriptive information shown in Appendix Table 13 indicates
that male repeaters are associated with higher levels of school disengagement at school than
female repeaters. Male repeaters also spend the least amount of hours on study among all
students. Second, our results in the previous section indicate that important mechanisms for the
spillovers might include social networks and joint activities together after school. Existing
literature consistently reveals gender differences in teenagers’ patterns of intimacy, where girls
are more likely to establish intimacy through discussion and self-disclosure whereas boys tend to
establish intimacy through shared activities (Bauminger et al. 2008; McNelles and Connolly
1999).
Table 7 presents the effects of having male and female repeater peers on each outcome and
mechanism measure of non-repeaters based on the model specification that controls for school
fixed effects, individual characteristics, homeroom teacher characteristics, and classroom
average peer characteristics.23
The results indicate that male repeaters primarily cause the
22
Given the rural-urban differences in school quality in China, we have conducted additional heterogeneity analysis
based on school location. The results are presented in Appendix Table 12 and follow similar patterns. 23
The proportion of male and female repeaters are calculated by dividing the number of male/female repeaters by
the total number of students in the class minus one. 46 repeaters have missing information on gender, and are thus
35
negative externalities on non-repeater students’ academic performance, cognitive assessment
score, school engagement, and educational expectations. For example, the coefficient for male
repeaters on non-repeaters’ academic performance (-0.028) implies that adding one male repeater
peer to a classroom of 46 students decreases non-repeater students’ test scores by nearly 5.6% of
one standard deviation. Estimates from other outcome variables predict that adding one more
male repeater peer to a classroom of 46 students decreases non-repeater students’ cognitive
assessment score by nearly 4.2% of one standard deviation, increases non-repeater students’
school disengagement by nearly 1.4% of one standard deviation, and decreases non-repeaters’
level of educational expectations by 1.6% of one standard deviation.24
Interestingly, when
focusing on after-school study hours, which is the most important mechanism identified in the
previous section, we also find that having a greater proportion of male repeaters in class reduces
non-repeaters’ own study hours but the same is not true for having greater proportions of female
repeaters. In addition, male repeaters also increase non-repeater peers’ probability of having
friends who play at internet cafés regularly, as well as having friends with general disciplinary
problems25
.
VI. Discussion and Conclusion
Understanding peer effects of low-ability children in the classroom is important, but
estimating peer effects credibly has been difficult due to data and methodological limitations. In
this study, we overcome these identification problems by utilizing nationally representative data
dropped from this analysis. Among repeaters who have non-missing information on gender (N=1,346), 785 (58%)
are male and 561 (42%) are female. 24
We also examine whether male repeaters have larger impact on male non-repeaters than female non-repeaters and
do not find any significant gender-matching effects. 25
Similar to our main analyses, we also conduct multiple hypothesis testing adjustments for our analyses that
differentiate between male and female repeaters. The adjusted p-values are presented in columns 4 and 6 in
Appendix Table 11. Although the adjustments lead to higher p-values in general, the estimated effects of male
Not enjoying life 0.011* 0.010* 0.007+ 0.006+ 6904
(0.005) (0.004) (0.004) (0.003)
Sad 0.008 0.007 0.003 0.004 6904
(0.005) (0.005) (0.005) (0.005)
Panel D: School disengagement I am often late for school 0.005 0.004 0.004 0.004 6969
(0.004) (0.004) (0.003) (0.003)
I am often absent from school 0.002 0.002 0.001 0.000 5825
(0.005) (0.005) (0.003) (0.003)
I seldom participate in school or class activities 0.011** 0.009* 0.006+ 0.007+ 7029
(0.004) (0.004) (0.003) (0.004)
I do not feel close to people at this school 0.016*** 0.015*** 0.011** 0.011** 7029
(0.004) (0.004) (0.004) (0.004)
I feel bored at school 0.014* 0.014* 0.011* 0.012* 7029
(0.006) (0.005) (0.005) (0.005)
I want to attend another school 0.012+ 0.012+ 0.007 0.008 7013
(0.006) (0.006) (0.006) (0.006)
Panel E: Educational expectations Expected years of education -0.014* -0.011+ -0.006 -0.003 7020
(0.006) (0.006) (0.005) (0.004)
Confidence about future -0.012** -0.010** -0.004 -0.004 7020 (0.004) (0.004) (0.004) (0.004) School fixed effects Yes Yes Yes Yes — Individual controls No Yes Yes Yes — Homeroom teacher controls No No Yes Yes — Classroom average peer controls No No No Yes —
Note: All outcome variables are standardized within non-repeaters within each school. Individual
controls, homeroom teacher controls, and classroom average peer controls are added in each specification.
Individual, homeroom teacher, and classroom average peer controls are the same with previous analyses.
School FE models. Standard errors in parentheses. + p < 0.10, * p<0.05, ** p<0.01, *** p<0.001.
67
Appendix Table 3
Descriptive Statistics of Homeroom Teacher and Classroom Characteristics
M
Homeroom teacher female 0.689
(0.464)
Homeroom teacher age in years 36.150
(7.196)
Education level
Professional college education 0.093
(0.291)
Adult higher education 0.366
(0.483)
College education or higher 0.541
(0.500)
Graduated from a normal university 0.907
(0.291)
Have a teaching certificate 0.995
(0.074)
Teaching experience in years 14.210
(9.010)
Teaching title
No title 0.115
(0.320)
Level 2 or 3 0.361
(0.482)
Level 1 0.377
(0.486)
Senior teacher or higher 0.148
(0.356)
Teaching award
School level or no award 0.262
(0.441)
County or district level 0.366
(0.483)
City level 0.257
(0.438)
Provincial or national level 0.115
(0.320)
Class size 46.360
(12.780)
Observations 183
Notes: Data are collapsed to class level. A normal university is a type of 4-year university in China that
specializes in teacher workforce training. Standard deviations in parentheses.
68
Appendix Table 4
Differences between Classrooms in Schools that Used Random Assignment and Those that Did Not
Random
assignment
Non-random
assignment
Raw gap
(1) (2) (3)
Panel A: School-level characteristics
Located in rural regions 0.344 0.562 -0.218+
(0.478) (0.512) (0.131)
School size 990.600 910.400 80.238
(693.600) (553.800) (194.704)
Average class size 45.640 45.880 -0.240
(12.430) (13.070) (3.597)
School funding in the current year per student
(RMB)
1074.200 872.000 202.167
(835.100) (410.700) (220.568)
Panel B: Student composition at school
Proportion of female students in school 0.468 0.454 0.013
(0.076) (0.036) (0.019)
Proportion of urban hukou students in school 0.473 0.392 0.081
(0.263) (0.277) (0.072)
Proportion of only-child students in school 0.432 0.439 -0.007
(0.271) (0.257) (0.073)
Student average age in school 13.580 13.570 0.005
(0.335) (0.272) (0.088)
Average mother education in years in school 9.659 9.598 0.062
(2.157) (1.682) (0.567)
Average father education in years in school 10.390 10.180 0.205
(1.824) (1.662) (0.488)
Proportion of low-income students in school 0.196 0.264 -0.068
(0.164) (0.186) (0.045)
69
Appendix Table 4
Differences between Classrooms in Schools that Used Random Assignment and Those that Did Not
(Continued)
Random assignment Non-random
assignment
Raw gap
(1) (2) (3)
Proportion of each mother occupation in school
Civil servants and government officials 0.030 0.027 0.003
(0.041) (0.032) (0.011)
Executive and managerial 0.054 0.034 0.020
(0.062) (0.043) (0.016)
Teachers, engineers, doctors, and lawyers 0.058 0.047 0.011